• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If the farmer sells 75 of his chickens, his stock of feed wi

This topic has 3 expert replies and 1 member reply

If the farmer sells 75 of his chickens, his stock of feed wi

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300

OA E

Source: Manhattan Prep

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
$$Let\ no\ of\ chicken=x$$
$$Let\ no\ of\ days=d$$
If the farmer sells 75 of his chicken, his stock of feed will last for 20 more days than planned
If he buys 100 more chicken, he will run out of feeds 15 days earlier than planned
$$Amount\ of\ feed\ =xd$$
$$xd=\left(x+100\right)\left(d-15\right)$$
$$where,\ xd=\left(x-75\right)\left(d+20\right)\ $$
$$\left(x-75\right)\left(d+20\right)\ =\left(x+100\right)\left(d-15\right)$$
$$\frac{\left(d+20\right)}{\left(d-15\right)}=\frac{\left(x+100\right)}{\left(x-75\right)}$$
$$\left(x=5d\right)$$
$$xd=\left(x-75\right)\left(d+20\right)$$
$$5d^2=\left(5d-75\right)\left(d+20\right)$$
$$d^2=\left(d-15\right)\left(d+20\right)$$
$$d=60$$
$$x=5d$$
$$x=5\cdot60=300$$
$$answer\ is\ OptionE$$

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
BTGmoderatorDC wrote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300

OA E

Source: Manhattan Prep
Let c = the number of chickens the farmer currently has and let d = the number of days he can feed the chickens. Notice that the number of chickens and the number of days the chicken can be fed with the constant amount of food the farmer has are inversely proportional. We can create the equations:

cd = (c - 75)(d + 20)

and

cd = (c + 100)(d - 15)

Simplifying the equations, we have:

cd = cd - 75d + 20c - 1500

cd = cd + 100d - 15c - 1500

Now adding the two equations, we have:

0 = -175d + 35c

175d = 35c

d = 35c/175 = c/5

Recall that cd = cd - 75d + 20c - 1500 or, simply, 0 = -75d + 20c - 1500. Now substitute c/5 for d, obtaining:

0 = -75(c/5) + 20c - 1500

0 = -15c + 20c - 1500

1500 = 5c

300 = c

Answer: E

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
BTGmoderatorDC wrote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300
Source: Manhattan Prep
$$\left( {\# {\rm{chicken}}} \right)\left( {\# days} \right) = {\rm{constant}}$$
$$? = x = \# {\rm{chicken}}$$
$$\left\{ \matrix{
\left( {x - 75} \right)\left( {d + 20} \right) = \left( {x + 100} \right)\left( {d - 15} \right)\,\,\,\,\left( {\rm{I}} \right) \hfill \cr
\left( {x - 75} \right)\left( {d + 20} \right) = xd\,\,\,\,\left( {{\rm{II}}} \right) \hfill \cr} \right.$$
$$\left( {\rm{I}} \right)\,\,\, \Rightarrow \,\,\,xd + 20x - 75d - 75 \cdot 20 = xd - 15x + 100d - 15 \cdot 100$$
$$ \Rightarrow \,\,\,35x - 175d = 20\left( {75 - 5 \cdot 15} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,35} \,\,\,\,\,x = 5d\,\,\,\left( {{\rm{III}}} \right)$$
$$\left( {{\rm{II}}} \right)\,\,\, \Rightarrow \,\,\,xd + 20x - 75d - 75 \cdot 20 = xd\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\rm{III}}} \right)} \,\,\,\,\,20x - {{75 \cdot x} \over 5} = 75 \cdot 20$$
$$ \Rightarrow \,\,\,5x = 75 \cdot 20\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 15 \cdot 20 = 300\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorDC wrote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300
Total amount of feed = (number of chickens)(number of days).
The number of chickens is INVERSELY PROPORTIONAL to the number of days.
If the number of chickens DOUBLES, then the feed will last for 1/2 the number of days.
If the number of chickens TRIPLES, then the feed will last for 1/3 the number of days.

Let f = feed, c = chickens, and d = days.
Thus:
f = cd.

Quote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned.
The colored portions and the answer choices indicate that the problem is constrained to POSITIVE INTEGERS.
The portions in blue imply that the value of c -- a value that must divide evenly into f -- is probably a multiple of 75 and 100.
The LCM of 75 and 100 is 300.
Thus, it is almost certain that c = a multiple of 300.

The portions in red imply that the value of d -- a value that also must divide evenly into f -- is probably a multiple of 20 and 15.
The LCM of 20 and 15 is 60.
Thus, it is almost certain that d = multiple of 60.

Of the five answer choices, only E is a multiple of 300.
Test E, letting c = 300 and d = 60, implying that f = 300*60 = 18,000.
When the correct answer is plugged in, the value of f will remain constant.

E: 300
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned.
(c-75)(d+20) = (300-75)(60+20) = (225)(80)= 18,000.
if he buys 100 more chickens, he will run out of feed 15 days earlier than planned.
(c+100)(d-15) = (300+100)(60-15) = (400)(45) = 18,000.
Success!
In each case, the value of f remains constant at 18,000.

The correct answer is E.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts